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1. Alternating sum of a linear sequence ●●○○○ 20 ptsThe $n$th term of a sequence is $a_n = (-1)^{n+1}(3n + 2)$. What is the value of $a_1 + a_2 + \dots + a_{100}$?
2. Erasing triples on a board ●●○○○ 20 ptsOn a board the numbers $1, 2, 3, \ldots, 27$ are written. One step consists of erasing three numbers $a, b, c$ from the board and writing in their place the number $a+b+c+n$, where $n$ is a fixed positive integer. Determine the positive integer $n$ such that, after 13 steps, the number $n^2$ is written on the board.